(1) Field of the Invention
The present invention relates to a method of controlling a plurality of satellites, and more particularly, to a satellite control method for maintaining a plurality of geostationary satellites at an identical longitude in which east-west velocity increment (NS coupling) during the execution of north-south orbit control is not negligible.
(2) Description of the Related Art
Satellites launched at an altitude of about 36,000 km above the equator of the earth synchronously revolve around the earth one rotation in about a day. Accordingly, when viewed from the earth, such satellites look as if they were fixed (stationary) at a point above the equator. Usually, however, the position of a geostationary satellite is not always the same, but the equatorial plane of the satellite may deviate from the equatorial plane or the semimajor axis of the orbit may vary due to the influence of various forces. Therefore, control operation is periodically executed to remedy such deviations. A control operation to move the satellite north or south toward the equatorial plane is called NS control, while a control operation to correct a deviation of the satellite within the orbital plane is called EW control. To achieve these control operations, the position of the satellite is monitored at all times from a ground station, and when position correction is required, a command is transmitted to the satellite to correct the orbit thereof. Satellites are equipped with thrusters for producing propelling forces, and their orbits are corrected by means of velocity increment vectors obtained through controlled injection of fuel from the thrusters.
Conventionally, when keeping a plurality of geostationary satellites at an identical longitude, particularly where the number of geostationary satellites is two, a method called longitude separation is generally employed. Since the position of a geostationary satellite is not always the same, a hold range is set and the satellite is controlled so as to be within the hold range. In the longitude separation method, the hold range is divided into two along the orbit and two satellites are positioned in respective subdivided ranges. For example, the sky in the vicinity of 110.degree. of east longitude is allotted to Japanese broadcasting satellites, and within a hold range of .+-.0.1.degree., one of the two satellites is positioned in a positive (+) 0.1.degree. range while the other is positioned in a negative (-) 0.1.degree. range.
Another method called orbital plane separation is also known wherein the orbital planes of respective satellites, i.e., the angles of inclination of the orbits, are made different from each other to avoid collision, thereby separating the orbital inclination angle vectors.
In the event the number of satellites becomes large and the longitude separation method or the orbital plane separation method is no longer applicable, a method called eccentricity separation can be used wherein a plurality of satellites is separated within a plane. The eccentricity separation method will be explained with reference to FIG. 5.
FIG. 5 illustrates a conventional sun-synchronous eccentricity separation method. A Cartesian coordinate system is defined with the earth at the center and a pair of mutually orthogonal axes .eta. and .xi.. In the illustrated example, four geostationary satellites A, B, C and D are positioned at the same longitude. Eccentricity vectors of the geostationary satellites A, B, C and D are indicted respectively at e.sub.A, e.sub.B, e.sub.C and e.sub.D. The eccentricity vector is a vector having a magnitude equal to the eccentricity and directed along the major axis of an ellipse in the direction of perigee. Perigee is the single point in an elliptical satellite orbit which is closest to the center of the earth. Since the four satellites have respective different eccentricities, they move along paths separated from one another but within the same hold range. The satellites are separated by their eccentricity, hence the method is called eccentricity separation. The eccentricity vectors are greatly influenced by the radiation pressure of the sun, and the points thereof describe circles a, b, c and d, respectively, in a year. Although the circles a, b, c and d intersect one another at several points, the points of the eccentricity vectors rotate synchronously during circling; therefore, the distances between the points of the vectors are always ensured and the satellites do not collide with one another. Thus the conventional eccentricity separation method utilizes the sun-synchronous rotation of the eccentricity. An outer circle R represents an allowable range for the eccentricity, and is calculated from the hold range of the stationary longitude. In other words, each satellite must remain in a respective stationary hold range with respect to a predetermined longitude. Thus, R represents an acceptable margin of error in the satellite orbit.
In large-sized three-axis attitude controlled satellites, variation in the eccentricity vector due to NS coupling is too large to be neglected, possibly causing the eccentricity vector to greatly deviate from the circle of rotation shown in FIG. 5. The NS coupling indicates the phenomenon that NS control for controlling the orbit north or south also affects the east-west position of the satellite. In the case of a box-shaped three-axis satellite, the time of execution of the NS control is long, and during this control period, the attitude of the satellite becomes unstable. To properly control the attitude, an EW control thruster automatically operates, thus changing the eastwest position of the satellite. Also when ejected gas impinges on a paddle and is reflected thereat, a propelling force in the EW direction is produced. Thus, when the NS control is executed, it eventually entails the EW control. Consequently, in some cases, a minimum inter-satellite distance cannot be secured. The point of the eccentricity vector rotates under the influence of the radiation pressure of the sun, as mentioned above, and the radius of the rotation is determined by the size (sectional area) and weight of the satellite.
Where the satellites to be controlled are large-sized three-axis attitude controlled satellites, the conventional sun-synchronous eccentricity separation method can only keep a maximum of three satellites in position, though eccentricity vector variations due to large NS coupling or the solar radiation pressure depend upon the performance of the propulsion system and the size and weight of the satellites.